Quartz crystal is widely used in an oscillator, a surface acoustic wave device for radiofrequency filters, an optical waveguide, a semiconductor substrate, etc. and is a very important material in industry.
Crystal modifications of silicon dioxide (SiO.sub.2) include quartz (.ltoreq.867.degree. C.), tridymite (867.degree. to 1,470.degree. C.), and cristobalite (1,470.degree. to 1,723.degree. C.). When these crystals are synthesized in practice, they are not always synthesized in an equilibrium state because of involvement of various factors such as impurities and temperature control, so that the above-described relationship between crystal structure and temperature does not always apply.
Quartz is a low-temperature phase (.ltoreq.870.degree. C.) of silicon dioxide crystals. However, since silicon dioxide has a melting point of 1,730.degree. C., which is far higher than the low-temperature phase transition point, 867.degree. C., it is deemed that solidification of molten silicon dioxide results in a glassy state or a crystal structure other than quartz, e.g., cristobalite which is stable around the melting point. Thus, it is considered that growth of quartz cannot be achieved by a simple high temperature treatment, and growth in low temperatures around the transition point be essential.
Aiming at growth of quartz in low temperatures below the transition point, quartz has conventionally been produced by a hydrothermal process in which crystal is produced from an aqueous solution under high temperature and high pressure conditions in a sealed container, particularly by a hydrothermal temperature differential process utilizing difference in temperature-dependent solubility of silicon dioxide in an alkali solution, in which a single crystal of quartz is made to grow on a seed crystal from an alkali solution of silicon dioxide by making a temperature difference under high temperature and high pressure conditions. The process for producing quartz by the hydrothermal temperature differential process is described, e.g., in Ceramics, vol. 15, 170-175 (1980).
However, the conventional hydrothermal temperature differential process requires large-scaled equipment, and cost saving cannot be afforded without using a huge apparatus and producing a large single crystal. Furthermore, the process only produces lumpy large crystals or particulate powder and cannot be applied as such to the formation of quartz single crystals having an arbitrary shape, such as a thin film. Therefore, quartz for actual use as an oscillator, a vibrator, a surface acoustic wave device for radiofrequency filters, etc. has been mass-produced by slicing a large-sized single quartz crystal produced by the hydrothermal temperature differential process.
With the recent heightening of telecommunication frequency, quartz having a further reduced thickness has been demanded for use as an oscillator, a vibrator or a filter. However, the thinness achieved by slicing of a large single crystal is limited, with the smallest thickness so far reached is 50 .mu.m in practice.
Further, in order to meet the above demand, a method for abrading quartz adhered on a semiconductor substrate into a thin film has been proposed as disclosed in JP-A-5-327383 (the term "JP-A" means an "unexamined published Japanese patent application"). Nevertheless, thickness reduction by abrasion is limited and incurs extra cost.